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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_density.wasp
Title produced by softwareKernel Density Estimation
Date of computationSun, 09 Feb 2014 17:33:57 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Feb/09/t13919852854i881kh9opprqiv.htm/, Retrieved Thu, 16 May 2024 13:45:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233530, Retrieved Thu, 16 May 2024 13:45:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Gemiddelde consum...] [2014-02-02 16:25:35] [30bd0864608e6e4b6d1ad83fb1317118]
- RMPD    [Kernel Density Estimation] [] [2014-02-09 22:33:57] [d660962d3573c8648285a9bf86237b1a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
7.72
7.67
7.84
7.79
7.83
7.94
8.02
8.06
8.12
8.13
7.97
8.01
8
7.9
7.99
8.02
8.08
8.02
8.07
8.11
8.19
8.16
8.08
8.22
8.15
8.19
8.31
8.3
8.34
8.31
8.38
8.34
8.44
8.64
8.6
8.61
8.54
8.69
8.73
8.91
9.01
9.08
8.94
9.03
9.02
8.96
9.03
8.94
8.95
8.95
8.99
8.93
8.98
8.95
9.02
8.92
9.1
9.06
8.97
8.89
8.99
8.79
8.83
8.61
8.71
8.91
8.91
8.89
8.98
9
8.99
8.88
8.93
8.96
9.21
9.08
9.11
9.12
9.2
9.43
9.64
9.72
9.72
9.62

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233530&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233530&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233530&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Properties of Density Trace
Bandwidth0.187521588640623
#Observations84

\begin{tabular}{lllllllll}
\hline
Properties of Density Trace \tabularnewline
Bandwidth & 0.187521588640623 \tabularnewline
#Observations & 84 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233530&T=1

[TABLE]
[ROW][C]Properties of Density Trace[/C][/ROW]
[ROW][C]Bandwidth[/C][C]0.187521588640623[/C][/ROW]
[ROW][C]#Observations[/C][C]84[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233530&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233530&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Properties of Density Trace
Bandwidth0.187521588640623
#Observations84






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.896940723649550.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.95907633092634 & 0.921878078427226 \tabularnewline
Epanechnikov & 8.92800852728795 & 0.845190768076698 \tabularnewline
Rectangular & 8.89694072364955 & 0.824691144385036 \tabularnewline
Triangular & 8.95286277019866 & 0.901783392269921 \tabularnewline
Biweight & 8.9404356487433 & 0.864898035278231 \tabularnewline
Cosine & 8.94664920947098 & 0.873464926299355 \tabularnewline
Optcosine & 8.92800852728795 & 0.85142382140971 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233530&T=2

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]8.95907633092634[/C][C]0.921878078427226[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.92800852728795[/C][C]0.845190768076698[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.89694072364955[/C][C]0.824691144385036[/C][/ROW]
[ROW][C]Triangular[/C][C]8.95286277019866[/C][C]0.901783392269921[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9404356487433[/C][C]0.864898035278231[/C][/ROW]
[ROW][C]Cosine[/C][C]8.94664920947098[/C][C]0.873464926299355[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.92800852728795[/C][C]0.85142382140971[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233530&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233530&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.896940723649550.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.903154284377230.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.95907633092634 & 0.921878078427226 \tabularnewline
Epanechnikov & 8.92800852728795 & 0.845190768076698 \tabularnewline
Rectangular & 8.90315428437723 & 0.824691144385036 \tabularnewline
Triangular & 8.95286277019866 & 0.901783392269921 \tabularnewline
Biweight & 8.9404356487433 & 0.864898035278231 \tabularnewline
Cosine & 8.94664920947098 & 0.873464926299355 \tabularnewline
Optcosine & 8.92800852728795 & 0.85142382140971 \tabularnewline
 \hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233530&T=3

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]8.95907633092634[/C][C]0.921878078427226[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.92800852728795[/C][C]0.845190768076698[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.90315428437723[/C][C]0.824691144385036[/C][/ROW]
[ROW][C]Triangular[/C][C]8.95286277019866[/C][C]0.901783392269921[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9404356487433[/C][C]0.864898035278231[/C][/ROW]
[ROW][C]Cosine[/C][C]8.94664920947098[/C][C]0.873464926299355[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.92800852728795[/C][C]0.85142382140971[/C][/ROW]
 [/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233530&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233530&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.903154284377230.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971






Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.909367845104910.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971

\begin{tabular}{lllllllll}
\hline
Maximum Density Values \tabularnewline
Kernel & x-value & max. density \tabularnewline
Gaussian & 8.95907633092634 & 0.921878078427226 \tabularnewline
Epanechnikov & 8.92800852728795 & 0.845190768076698 \tabularnewline
Rectangular & 8.90936784510491 & 0.824691144385036 \tabularnewline
Triangular & 8.95286277019866 & 0.901783392269921 \tabularnewline
Biweight & 8.9404356487433 & 0.864898035278231 \tabularnewline
Cosine & 8.94664920947098 & 0.873464926299355 \tabularnewline
Optcosine & 8.92800852728795 & 0.85142382140971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233530&T=4

[TABLE]
[ROW][C]Maximum Density Values[/C][/ROW]
[ROW][C]Kernel[/C][C]x-value[/C][C]max. density[/C][/ROW]
[ROW][C]Gaussian[/C][C]8.95907633092634[/C][C]0.921878078427226[/C][/ROW]
[ROW][C]Epanechnikov[/C][C]8.92800852728795[/C][C]0.845190768076698[/C][/ROW]
[ROW][C]Rectangular[/C][C]8.90936784510491[/C][C]0.824691144385036[/C][/ROW]
[ROW][C]Triangular[/C][C]8.95286277019866[/C][C]0.901783392269921[/C][/ROW]
[ROW][C]Biweight[/C][C]8.9404356487433[/C][C]0.864898035278231[/C][/ROW]
[ROW][C]Cosine[/C][C]8.94664920947098[/C][C]0.873464926299355[/C][/ROW]
[ROW][C]Optcosine[/C][C]8.92800852728795[/C][C]0.85142382140971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233530&T=4

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233530&T=4

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Maximum Density Values
Kernelx-valuemax. density
Gaussian8.959076330926340.921878078427226
Epanechnikov8.928008527287950.845190768076698
Rectangular8.909367845104910.824691144385036
Triangular8.952862770198660.901783392269921
Biweight8.94043564874330.864898035278231
Cosine8.946649209470980.873464926299355
Optcosine8.928008527287950.85142382140971


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 0 ; par2 = no ; par3 = 512 ;
Parameters (R input):
par1 = 0 ; par2 = no ; par3 = 512 ;
R code (references can be found in the software module):
if (par1 == '0') bw <- 'nrd0'
if (par1 != '0') bw <- as.numeric(par1)
par3 <- as.numeric(par3)
mydensity <- array(NA, dim=c(par3,8))
bitmap(file='density1.png')
mydensity1<-density(x,bw=bw,kernel='gaussian',na.rm=TRUE)
mydensity[,8] = signif(mydensity1$x,3)
mydensity[,1] = signif(mydensity1$y,3)
plot(mydensity1,main='Gaussian Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
mydensity1
bitmap(file='density2.png')
mydensity2<-density(x,bw=bw,kernel='epanechnikov',na.rm=TRUE)
mydensity[,2] = signif(mydensity2$y,3)
plot(mydensity2,main='Epanechnikov Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density3.png')
mydensity3<-density(x,bw=bw,kernel='rectangular',na.rm=TRUE)
mydensity[,3] = signif(mydensity3$y,3)
plot(mydensity3,main='Rectangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density4.png')
mydensity4<-density(x,bw=bw,kernel='triangular',na.rm=TRUE)
mydensity[,4] = signif(mydensity4$y,3)
plot(mydensity4,main='Triangular Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density5.png')
mydensity5<-density(x,bw=bw,kernel='biweight',na.rm=TRUE)
mydensity[,5] = signif(mydensity5$y,3)
plot(mydensity5,main='Biweight Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density6.png')
mydensity6<-density(x,bw=bw,kernel='cosine',na.rm=TRUE)
mydensity[,6] = signif(mydensity6$y,3)
plot(mydensity6,main='Cosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
bitmap(file='density7.png')
mydensity7<-density(x,bw=bw,kernel='optcosine',na.rm=TRUE)
mydensity[,7] = signif(mydensity7$y,3)
plot(mydensity7,main='Optcosine Kernel',xlab=xlab,ylab=ylab)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Properties of Density Trace',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Bandwidth',header=TRUE)
a<-table.element(a,mydensity1$bw)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'#Observations',header=TRUE)
a<-table.element(a,mydensity1$n)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Maximum Density Values',3,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Kernel',1,TRUE)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'max. density',1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,mydensity1$x[mydensity1$y==max(mydensity1$y)],1)
a<-table.element(a,mydensity1$y[mydensity1$y==max(mydensity1$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,mydensity2$x[mydensity2$y==max(mydensity2$y)],1)
a<-table.element(a,mydensity2$y[mydensity2$y==max(mydensity2$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,mydensity3$x[mydensity3$y==max(mydensity3$y)],1)
a<-table.element(a,mydensity3$y[mydensity3$y==max(mydensity3$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,mydensity4$x[mydensity4$y==max(mydensity4$y)],1)
a<-table.element(a,mydensity4$y[mydensity4$y==max(mydensity4$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,mydensity5$x[mydensity5$y==max(mydensity5$y)],1)
a<-table.element(a,mydensity5$y[mydensity5$y==max(mydensity5$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,mydensity6$x[mydensity6$y==max(mydensity6$y)],1)
a<-table.element(a,mydensity6$y[mydensity6$y==max(mydensity6$y)],1)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.element(a,mydensity7$x[mydensity7$y==max(mydensity7$y)],1)
a<-table.element(a,mydensity7$y[mydensity7$y==max(mydensity7$y)],1)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')
if (par2=='yes') {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Kernel Density Values',8,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'x-value',1,TRUE)
a<-table.element(a,'Gaussian',1,TRUE)
a<-table.element(a,'Epanechnikov',1,TRUE)
a<-table.element(a,'Rectangular',1,TRUE)
a<-table.element(a,'Triangular',1,TRUE)
a<-table.element(a,'Biweight',1,TRUE)
a<-table.element(a,'Cosine',1,TRUE)
a<-table.element(a,'Optcosine',1,TRUE)
a<-table.row.end(a)
for(i in 1:par3) {
a<-table.row.start(a)
a<-table.element(a,mydensity[i,8],1,TRUE)
for(j in 1:7) {
a<-table.element(a,mydensity[i,j],1)
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
}